A Second-row Parking Paradox

摘要

We consider two variations of the discrete car parking problem where at every vertex of ℤ cars (particles) independently arrive with rate one. The cars can park in two lines according to the following parking (adsorption) rules. In both models a car which arrives at a given vertex tries to park in the first line first. It parks (sticks) whenever the vertex and all of its nearest neighbors are not occupied yet. A car that cannot park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded. In the screening model a) a car cannot pass through parked cars in the second line with midpoints adjacent to its vertex of arrival.